Elliptic curve data - 5184.r2

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5184a', 'Clabel': '5184a3', 'Cnumber': 3, 'abc_quality': 1.1123490200903752, 'absD': 44530220924928, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [0, 0, 0, -6060, -368848], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 5184, 'degree': 8064, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3090888497175581459566884329', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 7, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-1159088625, 2097152], 'lmfdb_iso': '5184.r', 'lmfdb_label': '5184.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -852, 19664], 'min_quad_twist_disc': -24, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '12.8.0-3.a.1.3', '21.64.1.a.1', '24.16.0-24.a.1.2', '28.16.0-7.a.1.4', '56.32.0-56.a.1.3', '63.192.5.e.3', '84.128.1.?', '168.256.5.?', '252.384.5.?', '504.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0577358033807125082970016854', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 81], [3, 8, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.096836017345063048634241494928', 'prec': 110}, 'szpiro_ratio': 4.578265438067023, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, -2, 0, 0, 0, -3, 0, 1, 0], 'aplist': [0, 0, 0, 2, 3, -2, -3, 1, -6, -6, -4, 4, 9, 1, -6, -12, -3, -8, -5, -12, 11, -4, -12, 6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 5184, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '5184.r', 'trace_hash': 1284448247638606163}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.072935652480073593921102706450', 'prec': 107}, 'conductor': 5184, 'gens': [[17558, 2326528, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0577358033807125082970016854', 'prec': 100}], 'lmfdb_label': '5184.r2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25515985637143247861006093119', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1414851391353671351557866493829107497', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [17558]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 7, 0], '7': [1, 1], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '5184.r2'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 270659
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [3]}
  • id: 270660
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [2]}
  • id: 270664
    {'degree': 6, 'field': [-8, 0, 9, 0, 6, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [6]}
  • id: 270661
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [2, 2]}
  • id: 270662
    {'degree': 6, 'field': [24, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [3]}
  • id: 270663
    {'degree': 6, 'field': [224, 0, 1764, 0, 84, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [7]}
  • id: 270665
    {'degree': 12, 'field': [-8, 0, -33, 0, -27, 0, -6, 0, 6, 0, 3, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [4]}
  • id: 270667
    {'degree': 12, 'field': [98, 84, 54, 248, 201, -72, -54, 96, 72, -4, -12, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [2, 6]}
  • id: 270666
    {'degree': 12, 'field': [121, 396, 564, 432, 6, -72, 62, -72, 24, 0, 6, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [3, 3]}
  • id: 270668
    {'degree': 12, 'field': [14876, -67704, 89520, -19068, 17313, -8652, 1492, -420, 186, -28, -12, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [21]}
  • id: 270669
    {'degree': 18, 'field': [-128, 0, 0, 0, -576, 0, 2916, 0, -648, 0, 0, 0, -108, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [9]}
  • id: 270670
    {'degree': 18, 'field': [96, 0, 756, 0, 954, 0, -2799, 0, 1116, 0, 675, 0, -150, 0, -9, 0, 0, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [6]}
  • id: 270671
    {'degree': 18, 'field': [11239424, 0, 17912832, 0, -1712256, 0, -1859648, 0, 1101912, 0, 186396, 0, 9730, 0, -63, 0, 0, 0, 1], 'lmfdb_label': '5184.r2', 'torsion': [14]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 100847
    {'conductor': 5184, 'conductor_valuation': 6, 'discriminant_valuation': 39, 'j_denominator_valuation': 21, 'kodaira_symbol': -33, 'lmfdb_label': '5184.r2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 100848
    {'conductor': 5184, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '5184.r2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1697842
    {'adelic_gens': [[281, 392, 112, 393], [73, 402, 0, 1], [1, 426, 42, 253], [1, 216, 0, 1], [1, 0, 462, 1], [337, 168, 336, 169], [1, 0, 168, 1], [419, 462, 315, 461], [295, 42, 231, 211], [22, 321, 189, 169], [249, 226, 448, 345], [1, 0, 420, 1], [1, 168, 0, 1], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 5184, 'lmfdb_label': '5184.r2', 'prime': 0}
  • id: 25769
    {'conductor': 5184, 'elladic_image': '8.2.0.1', 'lmfdb_label': '5184.r2', 'modell_image': '2G', 'prime': 2}
  • id: 25770
    {'conductor': 5184, 'elladic_image': '3.4.0.1', 'lmfdb_label': '5184.r2', 'modell_image': '3B', 'prime': 3}
  • id: 25771
    {'conductor': 5184, 'elladic_image': '7.8.0.1', 'lmfdb_label': '5184.r2', 'modell_image': '7B', 'prime': 7}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 191883
    {'lmfdb_iso': '5184.r', 'p': 7, 'prec': 20, 'unit': 4325564754880312, 'val': 1}
  • id: 191884
    {'lmfdb_iso': '5184.r', 'p': 11, 'prec': 20, 'unit': 3577948907344260534, 'val': 2}
  • id: 191885
    {'lmfdb_iso': '5184.r', 'p': 13, 'prec': 20, 'unit': 740350937033637311687, 'val': 1}
  • id: 191886
    {'lmfdb_iso': '5184.r', 'p': 17, 'prec': 20, 'unit': 125906231272366247765953, 'val': 1}
  • id: 191887
    {'lmfdb_iso': '5184.r', 'p': 19, 'prec': 20, 'unit': 3678243717429057671239129, 'val': -1}
  • id: 191888
    {'lmfdb_iso': '5184.r', 'p': 23, 'prec': 20, 'unit': 66954701920351445525040888, 'val': 1}
  • id: 191889
    {'lmfdb_iso': '5184.r', 'p': 29, 'prec': 20, 'unit': 5748482761071479639165078278, 'val': 1}
  • id: 191890
    {'lmfdb_iso': '5184.r', 'p': 31, 'prec': 20, 'unit': 11356468796899421481240208138, 'val': 1}
  • id: 191891
    {'lmfdb_iso': '5184.r', 'p': 37, 'prec': 20, 'unit': 561370639235034683741249203794, 'val': 1}
  • id: 191892
    {'lmfdb_iso': '5184.r', 'p': 41, 'prec': 20, 'unit': 1766001807072394094659890195725, 'val': 1}
  • id: 191893
    {'lmfdb_iso': '5184.r', 'p': 43, 'prec': 20, 'unit': 290822337888193861664636405787436, 'val': -1}
  • id: 191894
    {'lmfdb_iso': '5184.r', 'p': 47, 'prec': 20, 'unit': 25543337073404075505598926230765, 'val': 1}
  • id: 191895
    {'lmfdb_iso': '5184.r', 'p': 53, 'prec': 20, 'unit': 116659118940175676280886726199639, 'val': 1}
  • id: 191896
    {'lmfdb_iso': '5184.r', 'p': 59, 'prec': 20, 'unit': 3255007344502777337283851628155597, 'val': 1}
  • id: 191897
    {'lmfdb_iso': '5184.r', 'p': 61, 'prec': 20, 'unit': 4054370912774498123218208098737019, 'val': 1}
  • id: 191898
    {'lmfdb_iso': '5184.r', 'p': 67, 'prec': 20, 'unit': 14031194624528006908290587515180339, 'val': 1}
  • id: 191899
    {'lmfdb_iso': '5184.r', 'p': 71, 'prec': 20, 'unit': 38212426506837775969262003208957677, 'val': 1}
  • id: 191900
    {'lmfdb_iso': '5184.r', 'p': 73, 'prec': 20, 'unit': 127884684476905834444569130546135605, 'val': 1}
  • id: 191901
    {'lmfdb_iso': '5184.r', 'p': 79, 'prec': 20, 'unit': 1116052777370419964429840626419982585, 'val': 1}
  • id: 191902
    {'lmfdb_iso': '5184.r', 'p': 83, 'prec': 20, 'unit': 1046192536661828179302767477166637596, 'val': 1}
  • id: 191903
    {'lmfdb_iso': '5184.r', 'p': 89, 'prec': 20, 'unit': 8159569290491582419321781712171674699, 'val': 1}
  • id: 191904
    {'lmfdb_iso': '5184.r', 'p': 97, 'prec': 20, 'unit': 37385125075643211201418955114603000073, 'val': 1}